Blade for high-performance shrouded propeller, multi-blade shrouded propeller provided with such blades and tail rotor arrangement with shrouded propeller for rotary wing aircraft

ABSTRACT

This invention relates to a blade for shrouded propeller, wherein: in plan, its aerodynamically active part presents a rectangular shape; and the maximum relative camber of the successive profiles constituting the aerodynamically active part of the blade increases from a value close to 0 to a value close to 0.04; the twist of the aerodynamically active part of the blade decreases from a first value close to 12° to a second value close to 4°, then increases to a third value close to 4.5°; and the maximum relative thickness of said successive profiles decreases from a value close to 13.5% to a value close to 9.5%.

FIELD OF THE INVENTION

The present invention relates to blades for high-performance shroudedpropellers, as well as to the shrouded propellers provided with aplurality of such blades. Its object is to increase the thrust or thepull delivered by such a shrouded propeller and, correlatively, toreduce the power necessary for driving this shrouded propeller inrotation. The present invention is particularly, but not exclusively,appropriate to be employed for auxiliary tail rotors of rotary wingaircraft.

BACKGROUND OF THE INVENTION

It is known that, with respect to a free propeller of the same diameter,a propeller shrouded in a duct theoretically makes it possible to obtaina substantially equal thrust or pull, with a gain in power of the orderof 30%.

In fact, the duct improves the yield of the propeller installed inside,with respect to a free propeller, for two reasons:

the circulation of the air through the duct creates a depression on theshroud and therefore a thrust of the fairing in its assembly, which issubstantially equal to the thrust of the propeller itself;

the flow in the vicinity of the shroud being in depression downstream ofthe propeller, the flux does not contract, contrarily to what occursdownstream of a free propeller, which has for its consequence toincrease the yield of the propeller, and this all the more so as thediffusion of the fluid stream is increased without stall in the shroud.

This is why, in numerous applications in which, in limited dimensions,it is question of creating a force of aerodynamic origin by a propeller,the solution of a shrouded propeller has proved more advantageous thanthat contributed by a free propeller.

Among such applications may be mentioned vertical take-off and landingaircraft, in which one or more vertical-axis shrouded propellers areintegrated in the fixed wing or fuselage; vehicles with lift byair-cushion, of which the pressurized air generators blowing towards theground are propellers housed inside fairings, themselves incorporated inthe body of the vehicle; and, finally, variable-pitch fans, for examplethose incorporated in a gas conduit in order to create a considerablecirculation of said gas in the conduit.

A particularly advantageous application has been made thereof to producethe tail rotor of helicopters.

It is known that, on such aircraft with lifting rotary wing, and inparticular on mechanically driven mono-rotor helicopters, in orderpermanently to balance the counter torque on the fuselage resulting fromthe rotation of the rotary wing, and in order to control the aircraft onits yaw axis, an auxiliary rotor is provided, disposed in the vicinityof the end of the tail of the aircraft and exerting a transverse thrustwhich is adaptable to all the flight conditions. This auxiliary tailrotor therefore exerts on the aircraft a balance torque of directionopposite the counter torque of the main rotor to its rotation by theengine or engines, i.e. in fact of the same direction as the drivingtorque of the lifting rotary wing.

Controlled variations of this balance torque by controlling the pitch ofthe blades of the anti-torque auxiliary rotor also enable the pilot tocontrol the course of the helicopter about its yaw axis.

However, and particularly on helicopters of low or average tonnage, theconventional anti-torque rotor constituted by a free propeller isparticularly vulnerable to outside aggressions: it may touch the groundstaff or touch the ground itself or any obstacle, all collisions whichdirectly compromise the balance of the helicopter and its safety inflight.

It is particularly in order to avoid these serious drawbacks thatApplicants have developed on helicopters of low and average tonnage, amultiblade tail rotor arrangement, shrouded inside the verticalstabilizer of these apparatus.

Such an installation is rendered possible and advantageous by the factthat the diameter of such a shrouded rotor may be relatively reducedwith respect to that of a free rotor of equivalent efficiency.

Such arrangements of anti-torque shrouded rotors are for exampledescribed in U.S. Pat. Nos. 3,506,219, 3,594,097 and 4,281,966.

Of course, it is sought to obtain from this auxiliary rotor, under theoptimum conditions of yield as far as the driving power is concerned, asufficiently high maximum thrust to satisfy the most demanding flightconditions and, by controlling the pitch of the blades, it is providedto take only a part of this maximum thrust adapted to the other flightcases.

It is known that the lifting efficiency of the rotary wings is generallycharacterized, for stationary operational conditions, by a parameterknown under the term of "figure of merit" which is the ratio between theminimum power for obtaining a given pull or thrust and the real powereffectively measured.

For a shrouded propeller, the expression of this parameter is given bythe following known formula: ##EQU1## in which FM is the figure ofmerit,

T the desired thrust or pull,

P the necessary power to be furnished to the propeller,

ρ the density of the air,

R the radius of the propeller, and

σ the coefficient of diffusion of the aerodynamic flux on the surface,this coefficient σ being equal to the ratio S∞/S, with S∞ representingthe surface of the flux at downstream infinite and S being the surfaceof the disc formed by the propeller in rotation.

In order to increase the figure of merit with fixed power anddimensions, it is therefore necessary to increase the thrust or pull ofthe propeller.

It is a particular object of the present invention to provide a bladefor shrouded propeller, of which the geometry of the aerodynamicallyactive part is optimalized so that the propeller delivers a thrust or apull which is as great as possible, whilst consuming a power which is alow as possible for drive thereof.

SUMMARY OF THE INVENTION

To that end, according to the invention, the blade for shroudedpropeller comprising a tunnel and a rotor with multiple blades coaxialto said tunnel, said rotor comprising a rotating hub of which the radiusis of the order of 40% that of said tunnel and on which said blades aremounted via blade shanks, is noteworthy:

in that, in plan, the aerodynamically active part of said bladepresents, beyond the blade shank, a rectangular shape with the resultthat the successive profiles constituting said aerodynamically activepart all have the same chord 1 and that the end section of saidaerodynamically active part is straight; and

in that, along the span of the blade counted from the axis of thetunnel, between a first section of which the relative span (i.e. withrespect to the total span of the blade) is close to 45% and the endsection of said blade:

the maximum relative camber of the successive profiles constituting saidaerodynamically active part of the blade is positive and increases froma value close to 0 to a value close to 0.04;

the twist of said aerodynamically active part of the blade decreasesfrom a first value close to 12° at said first section to a second valueclose to 4° at a second section of which the relative span is close to0.86, then increases from this second section to a third value close to4.5° at said end section of blade; and

the maximum relative thickness of said successive profiles decreasesfrom a value close to 13.5% to a value close to 9.5%.

Applicatns have, in fact, found that such a combination of evolutions ofcamber, of twist and of thickness of the profiles, associated with arectangular shape of the blades (the leading edge and the trailing edgebeing rectilinear and parallel), led to a blade presenting excellentaerodynamic properties (shown hereinafter) and excellent properties ofmechanical strength, in particular by an increase in the section ofblade in the vicinity of the root on the hub.

According to other advantageous features of the present invention:

(a) said maximum relative camber increases virtually linearly from thisvalue close to 0 to a value equal to 0.036 for a relative span equal to0.845, passing through values 0.01 and 0.02 respectively for therelative spans 0.53 and 0.66, then increases from this value equal to0.036 for the relative span equal to 0.845 up to a value equal to 0.038for the relative span equal to 0.93, and, finally, is constant and equalto 0.038 between the relative spans 0.93 and 1;

(b) the root of said blade presents evolutive profiles of which themaximum relative camber is negative and increases from a valuesubstantially equal to -0.013 for a relative span equal to 0.40 to saidvalue close to 0 for a relative span equal to 0.45;

(c) between the relative spans 0.45 and 1, the evolution of the twist isat least substantially parabolic, with a minimum at the relative span of0.86;

(d) the axis of twist of said aerodynamically active part is parallel tothe line of leading edge and to the line of trailing edge thereof and isdistant from said line of leading edge by a distance approximately equalto 39% of the length of the chord of the profiles;

(e) the twist of the root of said blade increases from said value closeto 8° for a relative span close to 0.38 to said value close to 12° forthe relative span equal to 0.45;

(f) the maximum relative thickness of the profiles decreases linearlyfrom a value close to 13.9% for a relative span equal to 0.40 to a valueclose to 9.5% for a relative span equal to 0.93, and is constant andequal to said value close to 9.5% between the relative spansrespectively equal to 0.93 and 1.

The profiles constituting said blades are preferably those which will bedefined hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be more readily understood on reading the followingdescription with reference to the accompanying drawings, in which:

FIG. 1 is a partial view of the rear part of a helicopter provided witha shrouded rotor arrangement generating a transverse air flow in orderto balance the driving torque of the main lifting rotor (not shown).

FIG. 2 is an enlarged section along line II--II of FIG. 1.

FIG. 3 shows in perspective a rotor blade according to the presentinvention.

FIGS. 4a, 4b and 4c are sections of the blade shown in FIG. 3,respectively along planes a--a, b--b and c--c thereof.

FIGS. 5a, 5b, 5c and 5d schematically illustrate, along the span of theblade counted from the axis of rotation X--X of the rotor, respectivelythe shape in plan of an embodiment of said blade, the variation ofrelative camber, the variation of the twist and the variation ofrelative thickness.

FIGS. 6a to 6e schematically show five profiles, referenced I to V,corresponding to five particular sections of the blade along its span.

FIG. 7 is a diagram showing the camber of profiles I to V of FIGS. 6a to6e.

FIG. 8 shows, as a function of the maximum coefficient of lift, thevariation of the figure of merit of a rotor equipped with bladesaccording to the invention, compared with a known rotor.

DETAILED DESCRIPTION OF THE DRAWINGS

referring now to the drawings, the helicopter tail 1 shown in FIGS. 1and 2 comprises a fuselage part 2 and a vertical stabilizer 3. At thebase of the vertical stabilizer 3 is arranged a tunnel 4 passing rightthrough the fuselage part 2, with the result that this tunnel comprisesan air intake 5 on one side of the fuselage and an air outlet 6 on theother side of said fuselage (cf. FIG. 2).

The tunnel 4 presents a shape of revolution about an axis X--X,transverse to the longitudinal axis L--L of the helicopter. For example,the air intake 5 presents a rounded peripheral edge 7 which is extended,towards the air outlet 6, by a cylindrical portion 8 itself extended upto said air outlet 6 by a divergent portion 9.

In tunnel 4 is mounted a rotating hub 10 provided with a plurality ofblades 11. This rotating hub 10 is borne by a fixed hub 12 fast with thestructure of the helicopter via three arms 13a, 13b and 13c. Therotating hub 10 and the fixed hub 12 are cylindrical in shape and arecentred on axis X--X of the tunnel 4. The rotating hub 10 is disposedtowards the air intake 5, so that, for example, the ends of the blades11 are located opposite the cylindrical portion 8 of the tunnel 4,whilst the fixed hub 12 is located towards the air outlet 6.

In known manner, inside the fixed hub 12 is located a mechanism 14 fordriving the rotating hub 10 in rotation, itself driven by a shaft 15,moved by the principal engine or engines (not shown) of the aircraftintended for driving the lifting rotary wing (likewise not shown). Inthis way, as explained hereinabove, the blades 11 of the rotating hub 10create the air flow which generates the transverse thrust necessary forthe equilibrium of the helicopter in yaw.

Likewise in known manner, in order to vary the intensity of thistransverse thrust, there is provided, inside the fixed hub 12 andpartially the rotating hub 10, a system 16 for controlling the angle ofpitch of the blades 11, actuated via a control rod 17.

The roots 18 of the blades 11 are mounted to rotate on the rotating hub10 and are connected to the pitch control system 16. Said blade roots 18are connected to the retaining and drive mechanism 14 by torsion bars19.

As shown in FIG. 2, one of the arms 13a for supporting the fixed hub 12serves as fairing for the shaft 15 and for the control rod 17.

The arms 13a, 13b and 13c may be uniformly distributed at 120° aboutaxis X--X and disposed with a certain relative offset to the rear of theplane of the blades 11.

FIG. 3 shows in perspective a blade 11 of the rotary hub 10, with itsblade root 18 and its torsion bar 19, disregarding said hub. Likewiseshown is the axis of rotation X--X of the rotating hub 10, as well as apart 27 of the means for fastening the bar 19, and therefore the blade11, to the retaining and drive mechanism 14.

The blade 11 comprises, in plan view, a rectilinear line of leading edge28. The line of trailing edge 29 is also rectilinear. In addition, therectilinear lines of leading edge 28 and of trailing edge 29 areparallel to each other.

In this way, in plan, the blade 11 presents a rectangular shape, with aconstant chord of profile 1 from the blade root 18 up to its outer endsection 30.

The blade 11 presents a span R, counted from the axis of rotation X--Xof the rotating hub 10. Hereinafter, the position in span of a profile(or of a section) of the blade 11 will be designated by the distance rseparating this profile (or this section) from the axis of rotation X--Xof said rotating hub 10, and more especially by the relative span r/Rcorresponding to this position.

The pitch control axis 31 of the blade 11 is parallel to lines 28 and 29of the leading edge and trailing edge.

The sections of the blade 11 shown in FIGS. 4a, 4b and 4c correspondrespectively to the planes of section a--a, b--b and c--c of FIG. 3,i.e. to planes of which the relative spans r/R with respect to axis X--Xare respectively equal to 100%, 73% and 45%.

The sections of FIGS. 4a, 4b and 4c show that the axis of twist v of theblade in span is merged with the pitch control axis 31 and that thisaxis of twist, which is distant from the leading edge line 28 by adistance d close to 39% of the length of the chord 1, passes through theplane of mid-thickness 32 of the corresponding profiles, this plane 32being parallel to the plane of the chords 33.

FIGS. 4a, 4b and 4c show, in addition, that the thickness, the twist andthe camber of the blade 11 vary considerably in span.

In the embodiment of a blade 11 according to the invention, illustratedby FIGS. 5a to 5d, it may be seen that the distance separating the axisX--X from the fastening means 27 is equal to 0.095 R, the torsion bar 19extends from 0.095 R to 0.38 R, the blade root 18 extends from 0.38 R to0.45 R and that the aerodynamically active part of the blade 11 properextends from 0.45 R to R.

The maximum relative camber K/1 (i.e. with respect to the chord 1) ofthe successive profiles constituting the aerodynamically active part ofsaid blade is negative and increases from a value equal to -0.013 forthe section of blade root 18 disposed at 0.40 R up to 0 for the sectionof blade root 18 disposed at 0.45 R. Between 0.45 R and 0.845 R, themaximum relative camber of the profiles of the aerodynamically activepart of the blade 11 increases considerably and regularly (andpreferably substantially linearly) from value 0 to a value close to0.036, passing through a value close to 0.01 for the section of bladedisposed at 0.53 R and through a value close to 0.02 for the sectionlocated at 0.66 R. Between 0.845 R and 0.93 R, the maximum relativechamber increases slightly from the value 0.036 to value 0.038, thenremains constant at this value 0.038 between 0.93 R and R (cf. FIG. 5b).

As illustrated in FIG. 5c, the twist v of the blade root 18 increasesconsiderably from 0.038 R to 0.45 R, passing from 8° to 11.9°. From 0.45R to 0.86 R, the twist of the blade 11 decreases from 11.9° to 3.7°,passing through values 6.99° at 0.61 R and 4.6° at 0.73 R. Finally, from0.86 R to R, the twist increases again from 3.7° to 4.6°. Between 0.45 Rand R, the variation of the twist v is preferably at least substantiallyparabolic.

The maximum relative thickness ₁ ^(e) of the blade root 18 and of theblade 11 decreases linearly from the value 13.9% for the sectiondisposed at 0.40 R to 9.5% for the section disposed at 0.93 R, passingthrough values 12.8%, 11.7% and 10.2% respectively for the sectionsdisposed at 0.53 R, 0.66 R and 0.845 R. Between 0.93 R and R, thisrelative thickness is constant and equal to 9.5% (cf. FIG. 5d).

In this way, in order to generate the blade 11 and its blade root 18, acertain number of basic profiles may be defined, intended to constituteddetermined sections thereof and to cause the intermediate profiles of aportion of blade included between two basic profiles, to evolveregularly, in order to satisfy the relative evolutions of thickness andof camber. It then suffices to set each of said basic profiles and saidintermediate profiles about the axis of twist 31 in order to obtain saidblade.

For example, to that end, five basic profiles may be defined, bearingrespective references I, II, III, IV and V hereinafter and presentingrespective maximum relative thicknesses equal to 9.5%, 10.2%, 11.7%,12.8% and 13.9%. Basic profile I will be used between R and 0.93 R,whilst profiles II, III, IV and V will be respectively disposed at thesections located at 0.845 R, 0.66 R, 0.53 R and 0.40 R. The definitionsof such profiles are given hereinafter with respect to a system ofrectangular axes OX, OY, which each have for origin the leading edge 28,the x-axis OX merging with the chord and being oriented from the leadingedge 28 towards the trailing edge 29 (for profiles I, II, III and IV) or34 (for profile V), as shown in FIGS. 6a to 6e.

A. Example of profile I having a maximum relative thickness equal to9.5% and usable between R and 0.93 R (cf. FIG. 6a)

Such a profile I may be such that:

the reduced ordinates of its upper surface line 35 are given

between X/1=0 and X/1=0.39433, by the formula

    Y/1=f1(X/1).sup.1/2 +f2(X/1)+f3(X/1).sup.2 +f4(X/1).sup.3 +f5(X/1).sup.4 +f6(X1).sup.5 +f7(X/1).sup.6                              (1)

with

f1=+0.16227

f2=-0.11704.10⁻¹

f3=+0.13247

f4=-0.25016.10

f5=+0.10682.10²

f6=-0.22210.10²

f7=+0.17726.10²

between X/1=0.39433 and X/1=1, by the formula

    Y/1=g0+g1(X/1)+g2(X/1).sup.2 +g3(X/1).sup.3 +g4(X/1).sup.4 +g5(X/1).sup.5 +g6(X/1).sup.6                                            (2)

with

g0=+0.22968

g1=-0.17493.10

g2=+0.77952.10

g3=-0.17457.10²

g4=+0.20845.10²

g5=-0.13004.10²

g6=+0.33371.10

whilst the reduced ordinates of the lower surface line 36 of the saidprofile are given

between X/1=0 and X/1=0.11862, by the formula

    Y/1=h1(X/1).sup.1/2 +h2(X/1)+h3(X/1).sup.2 +h4(X/1).sup.3 +h5(X/1).sup.4 +h6(X/1).sup.5 +h7(X/1).sup.6                             (3)

with

h1=-0.13971

h2=+0.10480.10⁻³

h3=+0.51698.10

h4=-0.11297.10³

h5=+0.14695.10⁴

h6=-0.96403.10⁴

h7=+0.24769.10⁵

between X/1=0.11862 and X/1=1, by the formula

    Y/1=i0+i1(X/1)+i2(X/1).sup.2 +i3(X/1).sup.3 +i4(X/1).sup.4 +i5(X/1).sup.5 +i6(X/1).sup.6                                            (4)

with

i0=-0.25915.10⁻¹

i1=-0.96597.10⁻¹

i2=+0.49503

i3=+0.60418.10⁻¹

i4=-0.17206.10

i5=+0.20619.10

i6=-0.77922

B. Example of profile II having a maximum relative thickness equal to10.2% and usable for a blade section disposed at 0.845 R (FIG. 6b)

For this profile II:

the reduced ordinates of the upper surface line 35 are given

between X/1=0 and X/1=0.39503, by the formula

    Y/1=j1(X/1).sup.1/2 +j2(X/1)+j3(X/1).sup.2 +j4(X/1).sup.3 +j5(X/1).sup.4 +j6(X/1).sup.5 +j7(X/1).sup.6                             (5)

with

j1=+0.14683

j2=-0.67115.10⁻²

j3=+0.44720

j4=-0.36828.10

j5=+0.12651.10²

j6=-0.23835.10²

j7=+0.18155.10²

between X/1=0.39503 and X/1=1, by the formula

    Y/1=k0+k1(X/1)+k2(X/1).sup.2 +k3(X/1).sup.3 +k4(X/1).sup.4 +k5(X/1).sup.5 +k6(X/1).sup.6                                            (6)

with

k0=+0.45955

k1=-0.39834.10

k2=+0.16726.10²

k3=-0.35737.10²

k4=+0.41088.10²

k5=-0.24557.10²

k6=+0.60088.10

whilst the reduced ordinates of the lower surface line 36 of saidprofile are given

between X/1=0 and X/1=0.14473, by the formula

    Y/1=m1(X/1).sup.1/2 +m2(X/1)+m3(X/1).sup.2 +m4(X/1).sup.3 +m5(X/1).sup.4 +m6(X/1).sup.5 +m7(X/1).sup.6                             (7)

with

m1=-0.13297

m2=-0.36163.10⁻¹

m3=+0.17284.10

m4=-0.27664.10²

m5=+0.30633.10³

m6=-0.16978.10⁴

m7=+0.36477.10⁴

between X/1=0.14473 and X/1=1, by the formula

    Y/1=n0+n1(X/1)+n2(X/1).sup.2 +n3(X/1).sup.3 +n4(X/1).sup.4 +n5(X/1).sup.5 +n6(X/1).sup.6                                            (8)

with

n0=-0.30824.10⁻¹

n1=-0.20564.10⁻¹

n2=-0.21738

n3=+0.24105.10

n4=-0.53752.10

n5=+0.48110.10

n6=-0.15826.10

C. Example of profile III having a relative maximum thickness equal to11.7% and usable for a blade section disposed at 0.66 R (FIG. 6c)

For this profile III,

the reduced ordinates of the upper surface line 35 are given

between X/1=0 and X/1=0.28515, by the formula

    Y/1=t1(X/1).sup.1/2 +t2(X/1)+t3(X/1).sup.2 +t4(X/1).sup.3 +t5(X/1).sup.4 +t6(X/1).sup.5 +t7(X/1).sup.6                             (9)

with

t1=+0.21599

t2=-0.17294

t3=+0.22044.10

t4=-0.26595.10²

t5=+0.14642.10³

t6=-0.39764.10³

t7=+0.42259.10³

between X/1=0.28515 and X/1=1, by the formula

    Y/1=u0+u1(X/1)+u2(X/1).sup.2 +u3(X/1).sup.3 +u4(X/1).sup.4 +u5(X/1).sup.5 +u6(X/1).sup.6                                            (10)

with

u0=+0.39521.10⁻¹

u1=+0.26170

u2=-0.47274

u3=-0.40872

u4=+0.15968.10

u5=-0.15222.10

u6=+0.51057

whilst the reduced ordinates of the lower surface line 36 of saidprofile are given

between X/1=0 and X/1=0.17428, by the formula

    Y/1=v1(X/1).sup.1/2 +v2(X/1)+v3(X/1).sup.2 +v4(X/1).sup.3 +v5(X/1).sup.4 +v6(X/1).sup.5 +v7(X/1).sup.6                             (11)

with

v1=-0.16526

v2=-0.31162.10⁻¹

v3=+0.57567.10

v4=-0.10148.10³

v5=+0.95843.10³

v6=-0.44161.10⁴

v7=+0.78519.10⁴

between X/1=0.17428 and X/1=1, by the formula

    Y/1=w0+w1(X/1)+w2(X/1).sup.2 +w3(X/1).sup.3 +w4(X/1).sup.4 +w5(X/1).sup.5 +w6(X/1).sup.6                                            (12)

with

w0=-0.25152.10⁻¹

w1=-0.22525

w2=+0.89038

w3=-0.10131.10

w4=+0.16240

w5=+0.46968

w6=-0.26400

D. Example of profile IV having a maximum relative thickness equal to12.8% and usable for a blade section disposed at 0.53 R (FIG. 6d)

For this profile IV,

the reduced ordinates of the upper surface line 35 are given

between X/1=0 and X/1=0.26861, by the formula

    Y/1=α1(X/1).sup.1/2 +α2(X/1)+α3(X/1).sup.2 +α4(X/1).sup.3 +α5(X/1).sup.4 +α6(X/1).sup.5 +α7(X/1).sup.6                                      (13)

with

α1=+0.19762

α2=+0.17213

α3=-0.53137.10

α4=+0.56025.10²

α5=-0.32319.10³

α6=+0.92088.10³

α7=-0.10229.10⁴

between X/1=0.26861 and X/1=1, by the formula

    Y/1=β0+β1(X/1)+β2(X/1).sup.2 +β3(X/1).sup.3 +β4(X/1).sup.4 +β5(X/1).sup.5 +β6(X/1).sup.6(14)

with

β0=+0.28999.10⁻¹

β1=+0.38869

β2=-0.10798.10

β3=+0.80848

β4=+0.45025

β5=-0.10636.10

β6=+0.47182

whilst the reduced ordinates of the lower surface line 36 of saidprofile are given

between X/1=0 and X/1=0.20934, by the formula

    Y/1=γ1(X/1).sup.1/2 +γ2(X/1)+γ3(X/1).sup.2 +γ4(X/1).sup.3 +γ5(X/1).sup.4 +γ6(X/1).sup.5 +γ7(X/1).sup.6                                      (15)

with

γ1=-0.25376

γ2=+0.61860

γ3=-0.96212.10

γ4=+0.12843.10³

γ5=-0.90701.10³

γ6=+0.32291.10⁴

γ7=-0.45418.10⁴

between X/1=0.20934 and X/1=1, by the formula

    Y/1=δ0+δ1(X/1)+δ2(X/1).sup.2 +δ3(X/1).sup.3 +δ4(X/1).sup.4 +δ5(X/1).sup.5 +δ6(X/1).sup.6(16)

with

δ0 =-0.25234.10⁻¹

δ1=-0.23995

δ2=+0.10890.10

δ3=-0.10066.10

δ4=-0.32520

δ5=+0.11326.10

δ6=-0.64043

E. Example of profile V having a maximum relative thickness equal to13.9% and usable for a section of blade root disposed at 0.40 R (FIG.6e)

For this profile V,

the reduced ordinates of the upper surface line 35 are given

between X/1=0 and X/1=0.19606, by the formula

    Y/1=ε1(X/1).sup.1/2 +ε2(X/1)+ε3(X/1).sup.2 +ε4(X/1).sup.3 +ε5(X/1).sup.4 +ε6(X/1).sup.5 +ε7(X/1).sup.6                                    (17)

with

ε1=+0.22917

ε2=-0.22972

ε3=+0.21262.10

ε4=-0.39557.10²

ε5=+0.32628.10³

ε6=-0.13077.10⁴

ε7=+0.20370.10⁴

between X/1=0.19606 and X/1=1, by the formula

    Y/1=λ0+λ1(X/1)+λ2(X/1).sup.2 +λ3(X/1).sup.3 +λ4(X/1).sup.4 +λ5(X/1).sup.5 +λ6(X/1).sup.6(18)

with

λ0=+0.32500.10⁻¹

λ1=+0.29684

λ2=-0.99723

λ3=+0.82973

λ4=+0.40616

λ5=-0.10053.10

λ6=+0.44222

whilst the reduced ordinates of the lower surface line 36 of saidprofile are given

between X/1=0 and X/1=0.26478, by the formula

    Y/1=μ1(X/1).sup.1/2 +μ2(X/1)+μ3(X/1).sup.2 +μ4(X/1).sup.3 +μ5(X/1).sup.4 +μ6(X/1).sup.5 +μ7(X/1).sup.6     (19)

with

μ1=-0.19314

μ2=-0.22031

μ3=+0.44399.10

μ4=-0.41389.10²

μ5=+0.23230.10³

μ6=-0.66179.10³

μ7=+0.74216.10³

between X/1=0.26478 and X/1=1, by the formula

    Y/1=ν0+ν1(X/1)+ν2(X/1).sup.2 +ν3(X/1).sup.3 +ν4(X/1).sup.4 +ν5(X/1).sup.5 +ν6(X/1).sup.6                       (20)

with

ν0=-0.42417.10⁻¹

ν1=-0.29161

ν2=+0.57883

ν3=+0.41309

ν4=-0.19045.10

ν5=+0.18776.10

ν6=-0.63583

FIG. 7 shows the evolution of the maximum relative camber K/1 of each ofsaid profiles I to V as a function of the reduced abscissa X/1.

These different profiles I to V, defined hereinabove with the aid ofspecific equations, in fact form part of a family of profiles of whicheach may be determined by a law of variation of thickness and a law ofcamber along the chord of the profile, in accordance with the techniquewhich is defined on page 112 of the report "Theory of wing sections" byH. ABOTT and E. VON DOENHOFF published in 1949 by McGRAW HILL BOOKCompany, Inc. and according to which the coordinates of a profile areobtained by plotting on either side of the median line andperpendicularly thereto, the half-thickness at that point.

In order to define the profiles of the family to which profiles I to Vbelong, the following analytic formulae are advantageously used for themedian line and the law of thickness:

for the median line:

    Y/1=c1(X/1)+c2(X/1).sup.2 +c3(X/1).sup.3 +c4(X/1).sup.4 +c5(X/1).sup.5 +c6(X/1).sup.6 +c7(X/1).sup.7                             (21)

for the law of thickness:

    ye/1=b1(X/1)+b2(X/1).sup.2 +b3(X/1).sup.3 +b4(X/1).sup.4 +b5(X/1).sup.5

     +b6(X/1).sup.6 +b7(X/1).sup.7 +b8(X/1).sup.8 +b9(X/1).sup.9 +b10(X/1).sup.10                                          (22)

For the profiles of the blades according to the invention, of which therelative thickness is included between 9% and 15%, each coefficient b1to b10 of formula (22) may advantageously be defined by correspondingformula (23.1) to (23.10), given hereinafter:

    b1=b11(e/1)+b12(e/1).sup.2 +b13(e/1).sup.3 +b14(e/1).sup.4 +b15(e/1).sup.5 +b16(e/1).sup.6                                           (23.1)

    b2=b21(e/1)+b22(e/1).sup.2 +b23(e/1).sup.3 +b24(e/1).sup.4 +b25(e/1).sup.5 +b26(e/1).sup.6                                           (23.2)

    b10=b101(e/1)+b102(e/1).sup.2 +b103(e/1).sup.3 +b104(e/1).sup.4 +b105(e/1).sup.5 +b106(e/1).sup.6                         (23.10)

The different coefficients b11 to b106 then have the following values:

    ______________________________________                                                  b11 = +0,98542.10.sup.5                                                       b12 = -0,43028.10.sup.7                                                       b13 = +0,74825.10.sup.8                                                       b14 = -0,64769.10.sup.9                                                       b15 = +0,27908.10.sup.10                                                      b16 = -0,47889.10.sup.10                                                      b21 = -0,33352.10.sup.7                                                       b22 = +0,14610.10.sup.9                                                       b23 = -0,25480.10.sup.10                                                      b24 = +0,22115.10.sup.11                                                      b25 = -0,95525.10.sup.11                                                      b26 = -0,16428.10.sup.12                                                      b31 = +0,39832.10.sup.8                                                       b32 = -0,17465.10.sup.10                                                      b33 = +0,30488.10.sup.11                                                      b34 = -0,26484.10.sup.12                                                      b35 = -0,11449.10.sup.13                                                      b36 = -0,19704.10.sup.13                                                      b41 = -0,24305.10.sup.9                                                       b42 = +0,10661.10.sup.11                                                      b43 = -0,18618.10.sup.12                                                      b44 = +0,16178.10.sup.13                                                      b45 = -0,69957.10.sup.13                                                      b46 = +0,12043.10.sup.14                                                      b51 = +0,86049.10.sup.9                                                       b52 = -0,37753.10.sup.11                                                      b53 = +0,65939.10.sup.12                                                      b54 = -0,57309.10.sup.13                                                      b55 = +0,24785.10.sup.14                                                      b56 = -0,42674.10.sup.14                                                      b61 = -0,18709.10.sup.10                                                      b62 = +0,82093.10.sup.11                                                      b63 = -0,14340.10.sup. 13                                                     b64 = +0,12464.10.sup.14                                                      b65 = -0,53912.10.sup.14                                                      b66 = +0,92831.10.sup.14                                                      b71 = +0,25348.10.sup.10                                                      b72 = -0,11123.10.sup.12                                                      b73 = +0,19432.10.sup.13                                                      b74 = -0,16892.10.sup.14                                                      b75 = +0,73066.10.sup.14                                                      b76 = -0,12582.10.sup.15                                                      b81 = -0,20869.10.sup.10                                                      b82 = +0,91583.10.sup.11                                                      b83 = -0,16000.10.sup.13                                                      b84 = +0,13909.10.sup.14                                                      b85 = -0,60166.10.sup.14                                                      b86 = +0,10361.10.sup.15                                                      b91 = +0,95554.10.sup.9                                                       b92 = -0,41936.10.sup.11                                                      b93 = +0,73266.10.sup.12                                                      b94 = -0,63693.10.sup.13                                                      b95 = +0,27553.10.sup.14                                                      b96 = -0,47450.10.sup.14                                                      b101 = -0,18663.10                                                            b102 = +0,81909.10.sup.10                                                     b103 = -0,14311.10.sup.12                                                     b104 = +0,12441.10.sup.12                                                     b105 = -0,58321.10.sup.13                                                     b106 = +0,92688.10.sup.13                                           ______________________________________                                    

Similarly, for maximum relative cambers of median line included between-2% and +5% of the chord, each coefficient c1 to c7 of formula (21)giving the pattern of the median line may advantageously be defined bycorresponding formula (24.1) to (24.7), given hereinafter:

    c1=c11(e/1)+c12(e/1).sup.2 -c13(e/1).sup.3 +c14(e/1).sup.4 +c15(e/1).sup.5 +c16(e/1).sup.6                                           (24.1)

    c2=c21(e/1)+c22(e/1).sup.2 +c23(e/1).sup.3 +c24(e/1).sup.4 +c25(e/1).sup.5 +c26(e/1).sup.6                                           (24.2)

    c7=c71(e/1)+c72(e/1).sup.2 +c73(e/1).sup.3 +c74(e/1).sup.4 +c75(e/1).sup.5 +c76(e/1).sup.6                                           (24.7)

The different coefficients c11 to c76 advantageously present thefollowing values:

    ______________________________________                                                  c11 = -0,29874.10.sup.1                                                       c12 = -0,61332.10.sup.2                                                       c13 = +0,60890.10.sup.5                                                       c14 = -0,43208.10.sup.6                                                       c15 = -0,12037.10.sup.9                                                       c16 = +0,24680.10.sup.10                                                      c21 = +0,17666.10.sup.2                                                       c22 = +0,70530.10.sup.4                                                       c23 = -0,40637.10.sup.6                                                       c24 = -0,28310.10.sup.8                                                       c25 = +0,20813.10.sup.10                                                      c26 = -0,31463.10.sup.11                                                      c31 = -0,38189.10.sup.3                                                       c32 = +0,31787.10.sup.2                                                       c33 = +0,23684.10.sup.4                                                       c34 = -0,47636.10.sup.8                                                       c35 = -0,26705.10.sup.10                                                      c36 = +0,65378.10.sup.11                                                      c41 = +0,13180.10.sup.4                                                       c42 = -0,44650.10.sup.5                                                       c43 = -0,65945.10.sup.7                                                       c44 = -0,35822.10.sup.9                                                       c45 = -0,24986.10.sup.10                                                      c46 = -0,58675.10.sup.11                                                      c51 = -0,18750.10.sup.4                                                       c52 = +0,72410.10.sup.5                                                       c53 = +0,90745.10.sup.7                                                       c54 = -0,54687.10.sup.9                                                       c55 = +0,58423.10.sup.10                                                      c56 = +0,50242.10.sup.11                                                      c61 = +0,12366.10.sup.4                                                       c62 = -0,43178.10.sup.5                                                       c63 = -0,61307.10.sup. 7                                                      c64 = +0,33946.10.sup.9                                                       c65 = -0,26651.10.sup.10                                                      c66 = -0,49209.10.sup.11                                                      c71 = -0,31247.10.sup.3                                                       c72 = -0,83939.10.sup.4                                                       c73 = +0,16280.10.sup.7                                                       c74 = -0,74431.10.sup.8                                                       c75 = +0,30520.10.sup.8                                                       c76 = -0,21265.10.sup.11                                            ______________________________________                                    

The above analytic formulae make it possible, once the evolution of thelaw of thickness as a function of the span of the blade (cf. FIG. 5d)and the evolution of the maximum camber with the span (cf. FIG. 5b) havebeen chosen, to define the geometry of the complete blade.

In order to check the efficiency of the present invention, a tail rotorarrangement, of the type described with reference to FIGS. 1 and 2, wasconstructed and the following experiments were carried out:

(a) Firstly, the rotary hub 10 was equipped with thirteen blades 11,each constituted by the constant NACA 63A312 profile, with constanttwist, and the curve giving the figure of merit FM of said arrangementwas plotted as a function of the mean coefficient of lift per blade Cz,which is defined by the formula ##EQU2## in which T, δ, ρ, 1 and R arerespectively the total thrust or pull of the rotor, the coefficient ofdiffusion of the aerodynamic flux, the density of the air, the chord ofthe blade and the radius of the propeller, as defined hereinabove, b isthe number of blades and U the peripheral speed of the propeller.

Curve A of FIG. 8 was obtained.

(b) The preceding thirteen blades were then replaced by thirteen bladesaccording to the present invention and the measurements were repeated.

Curve B of FIG. 8 was obtained.

These curves show that the maximum figure of merit FM and the maximummean coefficient of lift per blade of the rotor arrangement tested under(b) are respectively greater by 2.8% and by 8% with respect to thecorresponding magnitudes of the rotor arrangement tested under (a).

It is also seen from these curves that the improvement of the figure ofmerit is obtained whatever the mean load level per blade.

What is claimed is:
 1. A blade for shrouded propeller comprising atunnel and a rotor with multiple blades coaxial to said tunnel, saidrotor comprising a rotating hub of which the radius is of the order of40% that of said tunnel and on which said blades are mounted via bladeshanks, wherein:in plan, the aerodynamically active part of said bladepresents, beyond the blade shank, a rectangular shape with the resultthat the successive profiles constituting said aerodynamically activepart all have the same chord 1 and that the end section of saidaerodynamically active part is straight; and, along the span of theblade counted from the axis of the tunnel, between a first section ofwhich the relative span is close to 45% and the end section of saidblade:the maximum relative camber of the successive profilesconstituting said aerodynamically active part of the blade is positiveand increases from a value close to 0 to a value close to 0.04; thetwist of said aerodynamically active part of the blade decreases from afirst value close to 12° at said first section to a second value closeto 4° at a second section of which the relative span is close to 0.86,then increases from this second section to a third value close to 4.5°at said end section of blade; and the maximum relative thickness of saidsuccessive profiles decreases from a value close to 13.5% to a valueclose to 9.5%.
 2. The shrouded propeller blade of claim 1, wherein saidmaximum relative camber increases virtually linearly from this valueclose to 0 to a value equal to 0.036 for a relative span equal to 0.845,passing through values 0.01 and 0.02 respectively for the relative spans0.53 and 0.66, then increases from this value equal to 0.036 for therelative span equal to 0.845 up to a value equal to 0.038 for therelative span equal to 0.93, and, finally, is constant and equal to0.038 between the relative spans 0.93 and
 1. 3. The shrouded propellerblade of claim 1, wherein the root of said blade presents evolutiveprofiles of which the maximum relative camber is negative and increasesfrom a value substantially equal to -0.013 for a relative span equal to0.40 to said value close to 0 for a relative span equal to 0.45.
 4. Theshrouded propeller blade of claim 1, wherein, between the relative spans0.45 and 1, the evolution of the twist is at least substantiallyparabolic, with a minimum for the relative span of 0.86.
 5. The shroudedpropeller blade of claim 4, wherein the axis of twist of saidaerodynamically active part is parallel to the line of leading edge andto the line of trailing edge thereof and is distant from said line ofleading edge by a distance approximately equal to 39% of the length ofthe chord of the profiles.
 6. The shrouded propeller blade of claim 5,wherein the twist of the root of said blade increases from said valueclose to 8° for a relative span close to 0.38 to said value close to 12°for the relative span equal to 0.45.
 7. The shrouded propeller blade ofclaim 1, wherein the maximum relative thickness of the profilesdecreases linearly from a value close to 13.9% for a relative span equalto 0.40 to a value close to 9.5% for a relative span equal to 0.93, andis constant and equal to said value close to 9.5% between the relativespans respectively equal to 0.93 and
 1. 8. The shrouded propeller bladeof claim 7, wherein the portion of the aerodynamically active partincluded between the relative spans 0.93 and 1 is constituted by aprofile (I) having a maximum relative thickness equal to 9.5% and suchthat, as a function of the reduced abscissa X/1 along the chord, countedfrom the leading edge,the reduced ordinates of its upper surface line(35) are givenbetween X/1=0 and X/1=0.39433, by the formula

    Y/1=f1(X/1).sup.1/2 +f2(X/1)+f3(X/1).sup.2 +f4(X/1).sup.3 +f5(X/1).sup.4 +f6(X/1).sup.5 +f7(X/1).sup.6                             ( 1)

with f1=+0.16227 f2=-0.11704.10⁻¹ f3=+0.13247 f4=-0.25016.10f5=+0.10682.10² f6=-0.22210.10² f7=+0.17726.10² between X/1=0.39433 andX/1=1, by the formula

    Y/1=g0+g1(X/1)+g2(X/1).sup.2 +g3(X/1).sup.3 +g4(X/1).sup.4 +g5(X/1).sup.5 +g6(X/1).sup.6                                            ( 2)

with g0=+0.22968 g1=-0.17493.10 g2=+0.77952.10 g3=-0.17457.10²g4=+0.20845.10² g5=-0.13004.10² g6=+0.33371.10 whilst the reducedordinates of the lower surface line 36 of the said profile aregivenbetween X/1=0 and X/1=0.11862, by the formula

    Y/1=h1(X/1).sup.1/2 +h2(X/1)+h3(X/1).sup.2 +h4(X/1).sup.3 +h5(X/1).sup.4 +h6(X/1).sup.5 +h7(X/1).sup.6                             ( 3)

with h1=-0.13971 h2=+0.10480.10⁻³ h3=+0.51698.10 h4=-0.11297.10³h5=+0.14695.10⁴ h6=-0.96403.10⁴ h7=+0.24769.10⁵ between X/1=0.11862 andX/1=1, by the formula

    Y/1=i0+i1(X/1)+i2(X/1).sup.2 +i3(X/1).sup.3 +i4(X/1).sup.4 +i5(X/1).sup.5 +i6(X/1).sup.6                                            ( 4)

with i0=-0.25915.10⁻¹ i1=-0.96597.10⁻¹ i2=+0.49503 i3=+0.60418.10⁻¹i4=-0.17206.10 i5=+0.20619.10 i6=-0.77922.
 9. The shrouded propellerblade of claim 7, wherein the profile of the blade section disposed atthe relative span of 0.845 has a maximum relative thickness equal to10.2% and is such that, as a function of the reduced abscissa X/1 alongthe chord, counted from the leading edge,the reduced ordinates of theupper surface line (35) are givenbetween X/1=0 and X/1=0.39503, by theformula

    Y/1=j1(X/1).sup.1/2 +j2(X/1)+j3(X/1).sup.2 +j4(X/1).sup.3 +j5(X/1).sup.4 +j6(X/1).sup.5 +j7(X/1).sup.6                             ( 5)

with j1=+0.14683 j2=-0.67115.10⁻² j3=+0.44720 j4=-0.36828.10j5=+0.12651.10² j6=-0.23835.10² j7=+0.18155.10² between X/1=0.39503 andX/1=1, by the formula

    Y/1=k0+k1(X/1)+k2(X/1).sup.2 +k3(X/1).sup.3 +k4(X/1).sup.4 +k5(X/1).sup.5 +k6(X/1).sup.6                                            ( 6)

with k0=+0.45955 k1=-0.39834.10 k2=+0.16726.10² k3=-0.35737.10²k4=+0.41088.10² k5=-0.24557.10² k6=+0.60088.10 whilst the reducedordinates of the lower surface line (36) of said profile aregivenbetween X/1=0 and X/1=0.14473, by the formula

    Y/1=m1(X/1).sup.1/2 +m2(X/1)+m3(X/1).sup.2 +m4(X/1).sup.3 +m5(X/1).sup.4 +m6(X/1).sup.5 +m7(X/1).sup.6                             ( 7)

with m1=-0.13297 m2=+0.36163.10⁻¹ m3=+0.17284.10 m4=-0.27664.10²m5=+0.30633.10³ m6=-0.16978.10⁴ m7=+0.36477.10⁴ between X/1=0.14473 andX/1=1, by the formula

    Y/1=n0+n1(X/1)+n2(X/1).sup.2 +n3(X/1).sup.3 +n4(X/1).sup.4 +n5(X/1).sup.5 +n6(X/1).sup.6                                            ( 8)

with n0=-0.30824.10⁻¹ n1=-0.20564.10⁻¹ n2=-0.21738 n3=+0.24105.10n4=-0.53752.10 n5=+0.48110.10 n6=-0.15826.10.
 10. The shrouded propellerblade of claim 7, wherein the profile of the blade section disposed atthe relative span of 0.66 has a maximum relative thickness equal to11.7% and is such that, as a function of the reduced abscissa X/1 alongthe chord, counted from the leading edge,the reduced ordinates of theupper surface line are givenbetween X/1=0 and X/1=0.28515, by theformula

    Y/1=t1(X/1).sup.1/2 +t2(X/1)+t3(X/1).sup.2 +t4(X/1).sup.3 +t5(X/1).sup.4 +t6(X/1).sup.5 +t7(X/1).sup.6                             ( 9)

with t1=+0.21599 t2=-0.17294 t3=+0.22044.10 t4=-0.26595.10²t5=+0.14642.10³ t6=-0.39764.10³ t7=+0.42259.10³ between X/1=0.28515 andX/1=1, by the formula

    Y/1=u0+u1(X/1)+u2(X/1).sup.2 +u3(X/1).sup.3 +u4(X/1).sup.4 +u5(X/1).sup.5 +u6(X/1).sup.6                                            ( 10)

with u0=+0.39521.10⁻¹ u1=+0.26170 u2=-0.47274 u3=-0.40872 u4=+0.15968.10u5=-0.15222.10 u6=+0.51057 whilst the reduced ordinates of the lowersurface line of said profile are givenbetween X/1=0 and X/1=0.17428, bythe formula

    Y/1=v1(X/1).sup.1/2 +v2(X/1)+v3(X/1).sup.2 +v4(X/1).sup.3 +v5(X/1).sup.4 +v6(X/1).sup.5 +v7(X/1).sup.6                             ( 11)

with v1=-0.16526 v2=-0.31162.10⁻¹ v3=+0.57567.10 v4=-0.10148.10³v5=+0.95843.10³ v6=-0.44161.10⁴ v7=+0.78519.10⁴ between X/1=0.17428 andX/1=1, by the formula

    Y/1=w0+w1(X/1)+w2(X/1).sup.2 +w3(X/1).sup.3 +w4(X/1).sup.4 +w5(X/1).sup.5 +w6(X/1).sup.6                                            ( 12)

with w0=-0.25152.10⁻¹ w1=-0.22525 w2=+0.89038 w3=-0.10131.10 w4=+0.16240w5=+0.46968 w6=-0.26400.
 11. The shrouded propeller blade of claim 7,wherein the profile of the blade section disposed at the relative span0.53 R has a maximum relative thickness equal to 13.8% and is such that,as a function of the reduced abscissa X/1 along the chord, counted fromthe leading edge,the reduced ordinates of the upper surface line aregivenbetween X/1=0 and X/1=0.26861, by the formula

    Y/1=α1(X/1).sup.1/2 +α2(X/1)+α3(X/1).sup.2 +α4(X/1).sup.3 +α5(X/1).sup.4 +α6(X/1).sup.5 +α7(X/1).sup.6                                      ( 13)

with α1=+0.19762 α2=+0.17213 α=-
 0. 53137.10α4=+0.56025.10²α5=-0.32319.10³ α6=+0.92088.10³ α7=-0.10229.10⁴ between X/1=0.26861 andX/1=1, by the formula

    Y/1=β0+β1(X/1)+β2(X/1).sup.2 +β3(X/1).sup.3 +β4(X/1).sup.4 +β5(X/1).sup.5 +β6(X/1).sup.6( 14)

with β0=+0.28999.10⁻¹ β1=+0.38869 β2=-0.10798.10 β3=+0.80848 β4=+0.45025β5=-0.10636.10 β6=+0.47182 whilst the reduced ordinates of the lowersurface line of said profile are givenbetween X/1=0 and X/1=0.20934, bythe formula

    Y/1=γ1(X/1).sup.1/2 +γ2(X/1)+γ3(X/1).sup.2 +γ4(X/1).sup.3 +γ5(X/1).sup.4 +γ6(X/1).sup.5 +γ7(X/1).sup.6                                      ( 15)

with γ1=-0.25376 γ2=+0.61860 γ3=-0.96212.10 γ4=+0.12843.10³γ5=-0.90701.10³ γ6=+0.32291.10⁴ γ7=-0.45418.10⁴ between X/1=0.20934 andX/1=1, by the formula

    Y/1=δ0+δ1(X/1)+δ2(X/1).sup.2 +δ3(X/1).sup.3 +δ4(X/1).sup.4 +δ5(X/1).sup.5 +δ6(X/1).sup.6( 16)

with δ0=-0.25234.10⁻¹ δ1=-0.23995 δ2=+0.10890.10 δ3=-0.10066.10δ4=-0.32520 δ5=+0.11326.10 δ6=-0.64043.
 12. The shrouded propeller bladeof claim 7, wherein the profile of the section of blade root disposed atthe relative span of 0.40 has a maximum relative thickness equal to13.9% and is such that, as a function of the reduced abscissa X/1 alongthe chord, counted from the leading edge,the reduced ordinates of theupper surface line are givenbetween X/1=0 and X/1=0.19606, by theformula

    Y/1=ε1(X/1).sup.1/2 +ε2(X/1)+ε3(X/1).sup.2 +ε4(X/1).sup.3 +ε5(X/1).sup.4 +ε6(X/1).sup.5 +ε7(X/1).sup.6                                    ( 17)

with ε1=+0.22917 ε2=-0.22972 ε3=+0.21262.10 ε4=-0.39557.10²ε5=+0.32628.10³ ε6=-0.13077.10⁴ ε7=+0.20370.10⁴ between X/1=0.19606 andX/1=1, by the formula

    Y/1=λ0+λ1(X/1)+λ2(X/1).sup.2 +λ3(X/1).sup.3 +λ4(X/1).sup.4 +λ5(X/1).sup.5 +λ6(X/1).sup.6( 18)

with λ0=+0.32500.10⁻¹ λ=+
 0. 29684λ2=-0.99723 λ3=+0.82973 λ4=+0.40616λ5=-0.10053.10 λ6=+0.44222 whilst the reduced ordinates of the lowersurface line of said profile are givenbetween X/1=0 and X/1=0.26478, bythe formula

    Y/1=μ1(X/1).sup.1/2 +μ2(X/1)+μ3(X/1).sup.2 +μ4(X/1).sup.3 +μ5(X/1).sup.4 +μ6(X/1).sup.5 +μ7(X/1).sup.6     ( 19)

with μ1=-0.19314 μ2=-0.22031 μ3=+0.44399.10 μ4=-0.41389.10²μ5=+0.23230.10³ μ6=-0.66179.10³ μ7=+0.74216.10³ between X/1=0.26478 andX/1=1, by the formula

    Y/1=ν0+ν1(X/1)+ν2(X/1).sup.2 +ν3(X/1).sup.3 +ν4(X/1).sup.4 +ν5(X/1).sup.5 +ν6(X/1).sup.6                       ( 20)

with ν0=-0.42417.10⁻¹ ν1=-0.29161 ν2=+0.57883 ν3=+0.41309 ν4=-0.19045.10ν5=+0.18776.10 ν6=-0.63583.